st: mi impute chained with multilevel data

["Newport-berra, Mchale" <mnewport@jhsph.edu>]

I am using mi impute chained (Stata 12) to impute data for children nested in schools. I am then using the imputed data to do xtmixed. So far I have been able to do the multiple imputation without taking clustering into account, but  I would really appreciate guidance about how to account for the multi-level structure of the data in the imputation.  I have come across the following possibilities: 

One suggestion I have received is doing mi impute chained with a dataset of only the school-level variables, and then merging this with the child-level dataset and imputing the child-level variables.  However, I'm not sure how mi estimate would make sense of the imputed variables from different rounds of imputation.

Han  (2008, Developmental Psychology) used Stata and  assigned the same imputed values for school variables to students from the same school to preserve multilevel data structure in multiple imputation procedures, but I'm not sure how to do this.  

I also came across this Stata document: http://www.stata.com/support/faqs/statistics/clustering-and-mi-impute/ which describes the following 3 methods:

1. Include indicator variables for clusters in the imputation model
2. Impute data separately for each cluster.
3. Use a multivariate normal model to impute all clusters simultaneously.

Since I have a lot of schools but not a lot of kids in each school, #1 and #2 won't work. I'm not sure if #3 work with mi impute chained.

Has anyone used any of these strategies, or other strategies?  Thank you!






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